Data and codes for " A Unified Hybrid Deterministic-Stochastic Inversion Methodology" submitted to Jounal of Hydrology.

Accurate characterization of spatial heterogeneity in hydraulic properties is crucial for reliable groundwater modeling. Conventional approaches face a persistent trade-off between computational efficiency and characterization accuracy. Deterministic inversion with zonation offers computationalefficiencybut oversimplifies subsurface variability. Fully stochastic inversion without zonation or stochastic inversion with zonationcaptures heterogeneityin detail but can be computationally intensive andeven prohibitive for large-scale inverseproblems. To balance inversionaccuracy and computational efficiency, a mixed parameterization configuration is introduced, which involves delineating the model domain into multiple homogeneous and heterogeneous zones. This configuration encompasses diverse heterogeneity patterns such as zonal homogeneity, global heterogeneity, and zonal heterogeneity. Accordingly, a unified hybrid deterministic–stochastic (HDS) inversion methodology is proposed within ageostatistical inversion framework to flexibly support three conventional inversion strategies. When integrated with the Reduced-Order Successive Linear Estimator (ROSLE), the HDS-ROSLE approach achieves dimensionality reduction both conceptually and mathematically. A representative mixed configuration features a leaky aquifer system consisting of two homogeneous aquifers separated by a discontinuous, window-punctuated aquitard. A synthetic hydraulic tomography survey is performed for identifying the aquitard window. Four inversion strategies are implemented via the HDS-ROSLE approach. Comparative analysis reveals that the HDS inversiondelivers data-fitting performance comparable to those of fully stochastic and stochastic zonation inversions. Most significantly, the HDS inversion resolves the localized heterogeneity with lower uncertainty and substantially reduced computational cost. The inherent mixed structure provides a feasible foundation for the HDS inversion methodology to effectively characterize non-Gaussian fields.

准确刻画水力参数的空间非均质性，对于开展可靠的地下水数值模拟至关重要。传统方法始终面临计算效率与刻画精度之间的固有权衡难题。采用分区策略的确定性反演虽具备计算效率优势，但过度简化了地下介质的变异性；无分区全随机反演或带分区随机反演虽能细致捕捉非均质性，但计算量极大，在大规模反演问题中甚至会因计算成本过高而难以实施。为兼顾反演精度与计算效率，本文提出一种混合参数化方案：将模型域划分为多个均质与非均质分区，该方案可涵盖分区均质、全局非均质性与分区非均质性等多种非均质性模式。据此，本文在地质统计反演框架下提出了统一的混合确定性-随机反演（hybrid deterministic–stochastic，HDS）方法，可灵活支撑三类传统反演策略。当与降阶连续线性估计器（Reduced-Order Successive Linear Estimator，ROSLE）结合时，HDS-ROSLE方法可在概念与数学层面实现维度缩减。一个典型的混合参数化方案示例为越流含水层系统（leaky aquifer system）：该系统包含两个均质含水层（aquifer），二者之间由带有渗透窗口的间断式弱透水层（aquitard）分隔。针对该弱透水层的渗透窗口，开展了合成水力层析成像（hydraulic tomography）探测实验。基于HDS-ROSLE方法实现了四类反演策略。对比分析结果表明，HDS反演的数据拟合性能与全随机反演及带分区随机反演相当；尤为关键的是，HDS反演可在更低的不确定性下刻画局域非均质性，且计算成本大幅降低。其固有的混合结构为HDS反演方法有效刻画非高斯场提供了可行的基础。